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Whiteley N. Dimension-free Wasserstein contraction of nonlinear filters. Stoch Process Their Appl 2021. [DOI: 10.1016/j.spa.2021.01.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Lember J, Sova J. Exponential forgetting of smoothing distributions for pairwise Markov models. ELECTRON J PROBAB 2021. [DOI: 10.1214/21-ejp628] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Lehéricy L. Nonasymptotic control of the MLE for misspecified nonparametric hidden Markov models. Electron J Stat 2021. [DOI: 10.1214/21-ejs1890] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Luc Lehéricy
- Laboratoire J. A. Dieudonné, Université Côte d’Azur, CNRS, 06108, Nice, France
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Olsson J, Douc R. Numerically stable online estimation of variance in particle filters. BERNOULLI 2019. [DOI: 10.3150/18-bej1028] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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5
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Stability with respect to initial conditions in V-norm for nonlinear filters with ergodic observations. J Appl Probab 2017. [DOI: 10.1017/jpr.2016.90] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
AbstractWe establish conditions for an exponential rate of forgetting of the initial distribution of nonlinear filters in V-norm, allowing for unbounded test functions. The analysis is conducted in an general setup involving nonnegative kernels in a random environment which allows treatment of filters and prediction filters in a single framework. The main result is illustrated on two examples, the first showing that a total variation norm stability result obtained by Douc et al. (2009) can be extended to V-norm without any additional assumptions, the second concerning a situation in which forgetting of the initial condition holds in V-norm for the filters, but the V-norm of each prediction filter is infinite.
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Jasra A. On the Behaviour of the Backward Interpretation of Feynman-Kac Formulae Under Verifiable Conditions. J Appl Probab 2015. [DOI: 10.1239/jap/1437658602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We consider the time behaviour associated to the sequential Monte Carlo estimate of the backward interpretation of Feynman-Kac formulae. This is particularly of interest in the context of performing smoothing for hidden Markov models. We prove a central limit theorem under weaker assumptions than adopted in the literature. We then show that the associated asymptotic variance expression for additive functionals grows at most linearly in time under hypotheses that are weaker than those currently existing in the literature. The assumptions are verified for some hidden Markov models.
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On the Behaviour of the Backward Interpretation of Feynman-Kac Formulae Under Verifiable Conditions. J Appl Probab 2015. [DOI: 10.1017/s002190020001250x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
We consider the time behaviour associated to the sequential Monte Carlo estimate of the backward interpretation of Feynman-Kac formulae. This is particularly of interest in the context of performing smoothing for hidden Markov models. We prove a central limit theorem under weaker assumptions than adopted in the literature. We then show that the associated asymptotic variance expression for additive functionals grows at most linearly in time under hypotheses that are weaker than those currently existing in the literature. The assumptions are verified for some hidden Markov models.
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Travers NF. Exponential bounds for convergence of entropy rate approximations in hidden Markov models satisfying a path-mergeability condition. Stoch Process Their Appl 2014. [DOI: 10.1016/j.spa.2014.07.011] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Douc R, Moulines E, Olsson J. Long-term stability of sequential Monte Carlo methods under verifiable conditions. ANN APPL PROBAB 2014. [DOI: 10.1214/13-aap962] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Collet P, Leonardi F. Loss of memory of hidden Markov models and Lyapunov exponents. ANN APPL PROBAB 2014. [DOI: 10.1214/13-aap929] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Douc R, Moulines E. Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models. Ann Stat 2012. [DOI: 10.1214/12-aos1047] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Douc R, Garivier A, Moulines E, Olsson J. Sequential Monte Carlo smoothing for general state space hidden Markov models. ANN APPL PROBAB 2011. [DOI: 10.1214/10-aap735] [Citation(s) in RCA: 80] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Olsson J, Ströjby J. Particle-based likelihood inference in partially observed diffusion processes using generalised Poisson estimators. Electron J Stat 2011. [DOI: 10.1214/11-ejs632] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Douc R, Gassiat E, Landelle B, Moulines E. Forgetting of the initial distribution for nonergodic Hidden Markov Chains. ANN APPL PROBAB 2010. [DOI: 10.1214/09-aap632] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Olsson J, Cappé O, Douc R, Moulines É. Sequential Monte Carlo smoothing with application to parameter estimation in nonlinear state space models. BERNOULLI 2008. [DOI: 10.3150/07-bej6150] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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